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Integral domains with Booleant-class semigroup

✍ Scribed by S. Kabbaj; A. Mimouni


Book ID
113112313
Publisher
Springer-Verlag
Year
2012
Tongue
English
Weight
309 KB
Volume
1
Category
Article
ISSN
2193-5343

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πŸ“œ SIMILAR VOLUMES


Class semigroups of integral domains
✍ S. Kabbaj; A. Mimouni πŸ“‚ Article πŸ“… 2003 πŸ› Elsevier Science 🌐 English βš– 210 KB

This paper seeks ring-theoretic conditions of an integral domain R that reflect in the Clifford property or Boolean property of its class semigroup S(R), that is, the semigroup of the isomorphy classes of the nonzero (integral) ideals of R with the operation induced by multiplication. Precisely, in

t-class semigroups of integral domains
✍ Kabbaj, S; Mimouni, A πŸ“‚ Article πŸ“… 2007 πŸ› Walter de Gruyter GmbH & Co. KG 🌐 English βš– 341 KB
The class group of integral domains
✍ David F. Anderson; Gyu Whan Chang πŸ“‚ Article πŸ“… 2003 πŸ› Elsevier Science 🌐 English βš– 192 KB
Class Semigroups of PrΓΌfer Domains
✍ S Bazzoni πŸ“‚ Article πŸ“… 1996 πŸ› Elsevier Science 🌐 English βš– 218 KB

The class semigroup of a commutative integral domain R is the semigroup S S R of the isomorphism classes of the nonzero ideals of R with the operation induced by multiplication. The aim of this paper is to characterize the Prufer domains R Ε½ . such that the semigroup S S R is a Clifford semigroup, n